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Transverse Vibrations of Simple Rotor Systems
Published in Rajiv Tiwari, Rotor Systems: Analysis and Identification, 2017
The bearing force amplitude and phase can be obtained from Equation 2.143. Bearing reaction forces will have a similar trend in the variation with spin speed as that of the response, because it has the same denominator, Δ, as that of the response. It can be shown from Equation 2.143 that forces transmitted through bearings also have a maximum at system critical speeds. These forces are dynamic forces and are superimposed on any static loads that may be present, for example, due to gravity loading. In real systems that are designed to operate above their critical speeds, the machine would normally be run through the critical speed very quickly so that very large vibrations and forces associated with the resonance do not have sufficient time to build up. The same is true during the run-down where some form of braking may be employed. If the system is to run at the critical speed and vibrations are allowed to build up, then either the shaft will fracture and a catastrophic failure will result, or there may be sufficient damping in the system to simply limit the vibration and force amplitudes to some very large (albeit tolerable) value. It is common for some of the critical speeds to be suppressed for some combination of bearing parameters, and in Chapter 4 we will see such examples. Similarly, due to the presence of gyroscopic couple also critical speeds are suppressed, as we will see this in Chapter 5 and Chapter 11.
Stability and self-excited vibration of shafts
Published in Zbigniew Osiński, Damping of Vibrations, 2018
From the point of view of high-speed rotating shaft design, the critical speed related to the dynamic instability threshold is of great importance, since any value which exceeds this threshold can lead to the sudden growth of shaft vibration amplitude which may even result in damage of the machine. The critical speed can be controlled by the choice of physical and geometric parameters of a given system. Another, equally important problem is the behaviour of the system in the neighbourhood of the critical point. Self-excitation is known to have either a soft character (continuous, monotone growth of vibration amplitude) or a hard character (sudden jump of amplitude) with the appearance of near-critical vibration amplitude hysteresis.
Mechanical Construction of Switched Reluctance Machines
Published in Berker Bilgin, James Weisheng Jiang, Ali Emadi, Switched Reluctance Motor Drives, 2019
Yinye Yang, James Weisheng Jiang, Jianbin Liang
Different HEV and EV manufacturers have various preferences for their traction motors. New versions of traction motors are being developed for higher power, higher torque, higher maximum speed, and higher power density. These requirements can pose challenges on the shaft design. Higher power and torque usually require a larger shaft diameter and longer axial length. Higher power density means a more compact design, which might require a shorter shaft with a smaller diameter. For higher rotational speeds, the shaft should be designed to avoid the critical speed to reduce shaft vibration.
A new rotor balancing method using amplitude subtraction and its performance analysis with phase angle measurement-based rotor balancing method
Published in Australian Journal of Mechanical Engineering, 2020
A rotor is said to be unbalanced when axis of inertia of rotor does not coincide with axis of rotation of shaft. Balancing any rotor means coinciding (or try to coincide) the axis of inertial of the rotor and axis of rotation of the shaft (Khurmi and Gupta 2005). Theoretically, the inertia axis of the rotor coincides with axis of shaft, but in actual practice, this does not happen due to error in manufacturing process, wear and tear of rotating component, thermal deformations, deposition of material on rotor surface, etc. Rotor’s unbalance results in centrifugal couple and unbalance centrifugal forces that are being generated and transmitted to the shaft support bearings. These centrifugal couple and unbalance centrifugal forces further increases the value of centrifugal force, which further increases the distance of centre of gravity from axis of rotation. This effect is cumulative and ultimately the shaft fails. The bending of shaft not only depends upon the value of eccentricity but also depends upon the speed at which the shaft rotates. The speed, at which the shaft runs so that the additional deflection of the shaft from the axis of rotation becomes infinite, is known as critical speed (Khurmi and Gupta 2005). The forces generate vibrations in the machinery and this is why unbalance rotor is considered as one of the major factors that can lead to accelerating degradation of machine components or even catastrophic failure, especially at high speed where reliability is important consideration.
The impact of structural flexibilities of wheelsets and rails on the hunting behaviour of a railway vehicle
Published in Vehicle System Dynamics, 2019
Ingo Kaiser, Gerhard Poll, Gerhard Voss, Jordi Vinolas
The behaviour of the vehicle-track system is investigated for the scenario of permanent hunting; this behaviour is also known as ‘unstable hunting’, although this denomination is incorrect from the mathematical point of view. With respect to nonlinear system dynamics, the permanent hunting can be seen as an attractor; this attractor can be considered as a characteristic property of the system. Therefore, the consideration of the permanent hunting is useful for investigating the dynamic behaviour of the vehicle and its dependency on several influence factors, as already described in Section 1, although this behaviour is usually undesired in regular operation of the vehicle, since it can be associated with high dynamic forces causing damage to the track. Because of this, the lowest speed, at which permanent hunting occurs, is of high importance for the mechanical design of the vehicle; this speed is known as the nonlinear critical speed .
The influence of the active control of internal damping on the stability of a cantilever rotor with a disc
Published in Mechanics Based Design of Structures and Machines, 2022
In rotating systems it is very important to distinguish between the external (non-rotating) and internal (rotating) damping. External damping appears, e.g., in the supports or is caused by aerodynamic forces, and it always has a positive effect on the stability of rotating systems. On the other hand, the effect of internal damping, which results from energy dissipation in the rotor material or in/between other rotating elements, depends on the motion observed in the rotating frame. For rotation speeds below the first critical value, internal damping has a stabilizing effect. However, above the critical speed, it has a destabilizing influence, and there can appear regions in which the rotor is unstable.